46,784 research outputs found
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting
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Experimental and Numerical Investigation on Progressive Collapse Resistance of Post-tensioned Precast Concrete Beam-Column Sub-assemblages
In this paper, four 1/2 scaled precast concrete (PC) beam-column sub-assemblages with high performance connection were tested under push-down loading procedure to study the load resisting mechanism of PC frames subjected to different column removal scenarios. The parameters investigated include the location of column removal and effective prestress in tendons. The test results indicated that the failure modes of unbonded post-tensioned precast concrete (PTPC) frames were different from that of reinforced concrete (RC) frames: no cracks formed in the beams and wide opening formed near the beam to column interfaces. For specimens without overhanging beams, the failure of side column was eccentric compression failure. Moreover, the load resisting mechanisms in PC frames were significantly different from that of RC frames: the compressive arch action (CAA) developed in concrete during column removal was mainly due to actively applied pre-compressive stress in the concrete; CAA will not vanish when severe crush in concrete occurred. Thus, it may provide negative contribution for load resistance when the displacement exceeds one-beam depth; the tensile force developed in the tendons could provide catenary action from the beginning of the test. Moreover, to deeper understand the behavior of tested specimens, numerical analyses were carried out. The effects of concrete strength, axial compression ratio at side columns, and loading approaches on the behavior of the sub-assemblages were also investigated based on validated numerical analysis
Pairing fluctuation effects on the single-particle spectra for the superconducting state
Single-particle spectra are calculated in the superconducting state for a
fermionic system with an attractive interaction, as functions of temperature
and coupling strength from weak to strong. The fermionic system is described by
a single-particle self-energy that includes pairing-fluctuation effects in the
superconducting state. The theory reduces to the ordinary BCS approximation in
weak coupling and to the Bogoliubov approximation for the composite bosons in
strong coupling. Several features of the single-particle spectral function are
shown to compare favorably with experimental data for cuprate superconductors.Comment: 4 pages, 4 figure
Global behavior of cosmological dynamics with interacting Veneziano ghost
In this paper, we shall study the dynamical behavior of the universe
accelerated by the so called Veneziano ghost dark energy component locally and
globally by using the linearization and nullcline method developed in this
paper. The energy density is generalized to be proportional to the Hawking
temperature defined on the trapping horizon instead of Hubble horizon of the
Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the
fate of the universe and present the bifurcation phenomenon of the dynamical
system of the universe. It seems that the universe could be dominated by dark
energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE
Nonequilibrium nuclear-electron spin dynamics in semiconductor quantum dots
We study the spin dynamics in charged quantum dots in the situation where the
resident electron is coupled to only about 200 nuclear spins and where the
electron spin splitting induced by the Overhauser field does not exceed
markedly the spectral broadening. The formation of a dynamical nuclear
polarization as well as its subsequent decay by the dipole-dipole interaction
is directly resolved in time. Because not limited by intrinsic nonlinearities,
almost complete nuclear polarization is achieved, even at elevated
temperatures. The data suggest a nonequilibrium mode of nuclear polarization,
distinctly different from the spin temperature concept exploited on bulk
semiconductorsComment: 5 pages, 4 figure
Density-functional investigation of the rhombohedral to simple cubic phase transition of arsenic
We report on our investigation of the crystal structure of arsenic under
compression, focusing primarily on the pressure-induced A7 to simple cubic (sc)
phase transition. The two-atom rhombohedral unit cell is subjected to pressures
ranging from 0 GPa to 200 GPa; for each given pressure, cell lengths and
angles, as well as atomic positions, are allowed to vary until the fully
relaxed structure is obtained. We find that the nearest and next-nearest
neighbor distances give the clearest indication of the occurrence of a
structural phase transition. Calculations are performed using the local density
approximation (LDA) and the PBE and PW91 generalized gradient approximations
(GGA-PBE and GGA-PW91) for the exchange-correlation functional. The A7 to sc
transition is found to occur at 21+/-1 GPa in the LDA, at 28+/-1 GPa in the
GGA-PBE and at 29+/-1 GPa in the GGA-PW91; no volume discontinuity is observed
across the transition in any of the three cases. We use k-point grids as dense
as 66X66X66 to enable us to present reliably converged results for the A7 to sc
transition of arsenic.Comment: To be published in Physical Review B; material supplementary to this
article is available at arXiv:0810.169
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